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Quizzes > Mathematics > Algebra

Only for Geniuses: Take the Ultimate Math Quiz

Ready for this test of genius? Prove your algebra skills now!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
paper art illustration with math symbols and numbers floating over coral background for a genius level quiz

Attention genius-level problem solvers! This Only for Genius: Ultimate Math Quiz Challenge is your chance to dive into an exhilarating algebra challenge quiz and prove you're a true math whiz. Whether you're up for a brain-busting test of genius or a tough maths quiz, this free, scored math genius quiz will stretch your skills across number puzzles, equations, and logic twists. Join our online math quiz community, compare scores with fellow thinkers, and unlock new insights with fun genius trivia . Plus, instantly see how you rank against the sharpest minds. Ready to conquer? Start now and claim your bragging rights today!

What is the value of 7 + 8 2?
30
23
46
15
According to the order of operations, multiplication is performed before addition. Here you first calculate 8 2 = 16 and then add 7 to get 23. Misordering these steps leads to incorrect results. Order of Operations
Simplify the expression: (x + 3) - (2x - 5).
-x + 2
-x + 8
-x - 2
3x + 2
Distribute the minus sign over (2x - 5) giving x + 3 - 2x + 5, then combine like terms: x - 2x = -x and 3 + 5 = 8. Thus the simplified form is -x + 8. This method applies to subtracting any parentheses expressions. Combining Like Terms
What is the greatest common divisor (GCD) of 24 and 36?
6
12
18
4
The GCD is the largest integer that divides both numbers. Factors of 24 are {1,2,3,4,6,8,12,24} and of 36 are {1,2,3,4,6,9,12,18,36}. The greatest common element is 12. GCD Explained
Solve for x: 3x = 12.
4
3
6
-4
Divide both sides of the equation by 3 to isolate x: x = 12 3 = 4. This basic algebraic step removes the coefficient. Always perform the same operation on both sides of the equation. Solving Linear Equations
What is the next prime number after 11?
13
17
15
12
A prime number is divisible only by 1 and itself. After 11, the next integer is 12 (composite), then 13, which has no divisors other than 1 and 13. Hence 13 is the next prime. Prime Number Definition
Evaluate: 5^2 - 3^2.
16
4
7
10
Compute each power first: 5^2 = 25 and 3^2 = 9. Subtract 9 from 25 to get 16. Always evaluate exponents before subtraction. Exponents Properties
What is 50% of 80?
40
20
60
50
Fifty percent means one half of the value. Half of 80 is 40. Converting percentages to decimals (0.50 80) also yields 40. Percentage Calculations
If y = 2x and x = 5, what is y?
10
7
12
15
Substitute x = 5 into y = 2x to get y = 2 5 = 10. Function evaluation uses the current value of the variable. This is a direct substitution method. Function Evaluation
Solve for x: 2x + 5 = 17.
6
11
-6
7
Subtract 5 from both sides to get 2x = 12, then divide by 2 to find x = 6. Each operation preserves equality when applied to both sides. Linear Equations
Factor the expression: x^2 - 9.
(x - 3)(x + 3)
(x - 9)(x + 1)
(x - 3)^2
(x + 9)(x - 1)
This is a difference of squares: a^2 - b^2 = (a - b)(a + b). Here a = x and b = 3, giving (x - 3)(x + 3). Recognizing this pattern simplifies many algebraic expressions. Difference of Squares
Solve for x: (x/3) + 4 = 11.
21
7
33
-7
Subtract 4 from both sides to get x/3 = 7, then multiply by 3 to find x = 21. Ensuring each step is applied equally maintains the solution. Solving Linear Equations
Simplify the expression: 4(x - 2) + 6.
4x - 2
4x + 2
4x - 8
x - 2
First distribute 4 across (x - 2) to get 4x - 8, then add 6 yielding 4x - 2. Combining like terms produces the final result. Distributive Property
What is the least common multiple (LCM) of 4 and 6?
12
24
6
18
List multiples: 4 ? 4, 8, 12 and 6 ? 6, 12 The smallest common multiple is 12. LCM finds the smallest number divisible by both. LCM Explained
If f(x) = 2x^2 and x = 3, what is f(x)?
18
12
36
24
Substitute 3 into the function: f(3) = 2 (3)^2 = 2 9 = 18. Functions map inputs to outputs via the given rule. Function Evaluation
Solve the system: x + y = 10 and x - y = 2.
x = 6, y = 4
x = 4, y = 6
x = 2, y = 8
x = 8, y = 2
Add the equations: (x + y) + (x - y) = 10 + 2 gives 2x = 12, so x = 6. Substitute back to find y = 4. This is the elimination method. System of Equations
What is the slope of the line passing through (1, 2) and (3, 6)?
2
4/2
3/2
-2
Slope = (y2 - y1) / (x2 - x1) = (6 - 2) / (3 - 1) = 4 / 2 = 2. This ratio measures the steepness of the line. Slope of a Line
Solve for x: x^2 - 5x + 6 = 0.
x = 2 or x = 3
x = -2 or x = -3
x = 1 or x = 6
x = 5 or x = 6
Factor the quadratic: (x - 2)(x - 3) = 0, so x = 2 or x = 3. Quadratic factoring finds roots efficiently. Factoring Quadratics
What is the sum of the interior angles of a convex hexagon?
720
540
360
900
For any n-sided polygon, the sum is (n - 2) 180. Here n = 6, so (6 - 2) 180 = 720. This formula applies to all convex polygons. Interior Angle Sum
Evaluate the expression: 3^3 2^4.
432
216
648
384
Compute powers separately: 3^3 = 27 and 2^4 = 16, then multiply: 27 16 = 432. Carrying out exponentiation before multiplication is key. Exponent Rules
If a fair die is rolled twice, what is the probability of getting two even numbers?
1/4
1/2
1/8
1/3
Each roll has a 3/6 = 1/2 chance of being even. The events are independent, so multiply probabilities: (1/2) (1/2) = 1/4. This is a basic rule of probability. Basic Probability
Simplify the rational expression: (2x^3 y^2) / (4x y).
x^2 y / 2
x^2 y / 4
x^2 y^2 / 2
x^3 y
Divide coefficients: 2/4 = 1/2. Subtract exponents: x^(3?1) = x^2, y^(2?1) = y. Thus result is (x^2 y)/2. Laws of exponents apply to both variables. Exponent Properties
Find the determinant of the matrix [[2, 3], [1, 4]].
5
2
7
-5
For a 22 matrix [[a, b], [c, d]], the determinant is ad - bc. Here 24 - 31 = 8 - 3 = 5. Determinants measure area scaling or matrix invertibility. Determinant Formula
Solve for x: sqrt(x + 3) = 5.
22
2
25
-22
Square both sides: x + 3 = 25, so x = 22. Check domain: x + 3 ? 0 holds when x = 22. Always verify solutions in the original equation. Radical Equations
How many 5-digit numbers have digits that sum to 5?
126
70
35
210
We count nonnegative solutions to d1 + d2 + d3 + d4 + d5 = 5 with 1 ? d1 ? 9. Let d1' = d1 - 1, then d1' + d2 + d3 + d4 + d5 = 4. The number of solutions is C(4 + 5 - 1, 5 - 1) = C(8,4) = 70. This uses the stars and bars method. Stars and Bars
What is the general solution to the recurrence relation a? = 3a??? ? 2 with a? = 4?
3 2? + 1
3 3? + 1
4 3? ? 2
3? + 2
Solve the homogeneous part a?^h = C3? and find a particular solution a?^p = 1. General solution: a? = C3? + 1. Use a? = 4 to get C + 1 = 4, so C = 3. Hence a? = 33? + 1. Recurrence Relations
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Study Outcomes

  1. Analyze Complex Algebraic Expressions -

    Break down and simplify advanced equations to sharpen your skills in the algebra challenge quiz.

  2. Solve Numerical Puzzles Quickly -

    Apply strategic methods to tackle number-based challenges under time constraints in this tough maths quiz.

  3. Evaluate Your Math Genius Skills -

    Interpret your results from the math genius quiz to identify strengths and areas for improvement.

  4. Apply Logical Reasoning Techniques -

    Use pattern recognition and deduction to solve the most demanding problems in the test of genius.

  5. Benchmark Against Genius-Level Criteria -

    Compare your performance to only for genius standards to see if you meet the ultimate challenge threshold.

  6. Develop Advanced Problem-Solving Strategies -

    Refine and adapt methods for future algebra challenge quizzes and other high-level math tests.

Cheat Sheet

  1. Quadratic Equations & Vieta's Formulas -

    Master the standard form ax²+bx+c=0 and use Vieta's relations (sum of roots = - b/a, product = c/a) for lightning-fast solutions (MIT OpenCourseWare). For example, x² - 5x+6=0 gives roots 2 and 3 in one step. A handy mnemonic is "sum is negative b, product is c" to stay sharp in this only for genius level challenge.

  2. Arithmetic & Geometric Sequences -

    Review the nth-term formulas aₙ=a₝+(n - 1)d for arithmetic and gₙ=a₝·r❿❻¹ for geometric sequences (Khan Academy). Practice sum formulas Sₙ= n/2·(2a₝+(n - 1)d) and Sₙ=a₝(1 - r❿)/(1 - r) in quick drills. Mnemonic: "Add or multiply your way through" - perfect prep for any tough maths quiz.

  3. Modular Arithmetic & Congruences -

    Work with remainders using statements like 17≡2 mod 5 and solve puzzles via the Chinese Remainder Theorem (Art of Problem Solving). Treat mods like clock arithmetic to simplify huge exponent problems (e.g., 7¹❰❰ mod 5). This test of genius staple will boost your number theory confidence.

  4. Functional Equations & Symmetry Tricks -

    Spot patterns by plugging special values (x=0,1, - 1) and look for symmetry to guess linear or quadratic forms (USAMO problems archive). For f(x+1)=f(x)+2x+1, assume f(x)=ax²+bx+c and match coefficients. A playful tip: draw a quick table to see if f behaves like a parabola or a line.

  5. Factorization & Prime Magic -

    Sharpen skills with identities like a² - b²=(a - b)(a+b) and sum/difference of cubes: a³±b³=(a±b)(a²∓ab+b²) (Encyclopaedia of Mathematics). Break down large numbers into primes to solve puzzles on divisibility and LCM/GCD. Use the "SOAP" mnemonic (Same, Opposite, Always Positive) for sums/differences of odd powers.

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